Sparse estimators for multivariate integer-valued autoregressive models with applications to inference for Hawkes processes

Networks are ubiquitous throughout biology, spanning the entire range from molecules to food webs and global environmental systems. Yet, despite substantial efforts by the scientific community, the inference of these networks from data still presents a problem that is unsolved in general. One frequent strategy of addressing the structure of networks is the assumption that the interactions among molecular or organismal populations are static and correlative. While often successful, these static methods are no panacea. They usually ignore the asymmetry of relationships between two species and inferences become more challenging if the network nodes represent dynamically changing quantities. Overcoming these challenges, two very different network inference approaches have been proposed in the literature: Lotka-Volterra (LV) models and Multivariate Autoregressive (MAR) models. These models are computational frameworks with different mathematical structures which, nevertheless, have both been proposed for the same purpose of inferring the interactions within coexisting population networks from observed time-series data. Here, we assess these dynamic network inference methods for the first time in a side-by-side comparison, using both synthetically generated and ecological datasets. Multivariate Autoregressive and Lotka-Volterra models are mathematically equivalent at the steady state, but the results of our comparison suggest that Lotka-Volterra models are generally superior in capturing the dynamics of networks with non-linear dynamics, whereas Multivariate Autoregressive models are better suited for analyses of networks of populations with process noise and close-to linear behavior. To the best of our knowledge, this is the first study comparing LV and MAR approaches. Both frameworks are valuable tools that address slightly different aspects of dynamic networks.

This project assessed the use of multivariate auto-regressive (MAR) models to create forecasts of continuous vital signs in hospitalized patients. A total of 20 hours continuous (1/60Hz) heart rate and respiration rate from eight postoperative patients, where used to fit a centered MAR model for forecasting in windows of 15 minutes. The model was fitted using Markov Chain Monte Carlo sampling, and the model was evaluated on data from five additional patients. The results demonstrate an average RMSE in the forecast window of 11.4 (SD: 7.30) beats per minute for heart rate and 3.3 (SD:1.3) breaths per minute for respiration rate. These results indicate potential for forecasting vital signs in a clinical setting.

The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying lengths (T = 25, 50, 75, 100, 125) using Statistical Analysis System (SAS) version 9.2. Autoregressive components for the 5 series vectors included coefficients of .80, .70, .65, .50 and .40. Error variance components included values of .20, .20, .10, .15, and .15, with cross-lagged coefficients of .10, .10, .15, .10, and .10. A Monte Carlo study revealed that in comparison to frequentist methods, the Bayesian approach provided increased sensitivity for hypothesis testing and detecting Type I error.

This study developed a driving mental fatigue estimation system based on electroencephalogram (EEG) when he drives a car in a virtual reality (VR)-based dynamic simulator. To classify driver's mental fatigue status, the features of multichannel electroencephalographic (EEG) signals of frontal, central and occipital are extracted by multivariate autoregressive (MVAR) model. Then kernel principal component analysis (KPCA) and support vector machines (SVM) are combined to identify three-levels driving mental fatigue. The results show that KPCA is an good feature extractor which can effectively reduce the dimensionality of the feature vectors. The KPCA-SVM shows good performance with higher classification accuracy (81.64%) across 10 subjects. This method could be an potential approach of classification of driving mental fatigue.

Event Abstract Back to Event Characterizing fetal sympatho-vagal balance through multivariate time-varying autoregressive modeling of magnetocardiographic data D. Gutiérrez1*, F M García-Guevara1, I Kiefer2, R. Draganova2 and H Preissl2 1 Centro de Investigación y de Estudios Avanzados, Mexico 2 MEG-Center, Germany We propose a method to analyze fetal beat-to-beat heart rate variability (HRV) obtained from magnetocardiographic (MCG) measurements at different times of gestation using a multivariate time-varying autoregressive (MTVAR) model. Our approach is based on treating a group of HRV signals from a single fetus and measured at different gestational periods as a dynamical system, from which we obtain a suitable MTVAR model. This kind of autoregressive model has been previously found useful to study the dynamics of multichannel data associated to brain activity. Then, changes in the values of the coefficients of the MTVAR model obtained from the HRV signals can be associated to changes in fetal sympatho-vagal balance. Therefore, in this paper we propose to characterize the variations in the sympatho-vagal balance at specific gestational period by comparing the dynamics of the MTVAR coefficients to the SDNN/RMSSD ratio, which is known to be a potential marker for sympatho-vagal balance. Furthermore, an overall behavior of the sympatho-vagal balance during the gestation (or at least over the weeks when measurements were acquired) could be estimated from the average values of the MTVAR coefficients by comparing them to the tendencies obtained through the classical analysis of the different frequency bands in the HRV signal. In order to demonstrate the applicability of the proposed modeling approach, real magnetocardiographic data from healthy fetuses is analyzed. Preliminary results show that the MTVAR model is able to mimic the sympatho-vagal development reported in the literature, and the results also show consistency independently of the number of gestational periods used in the analysis. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: Fetal and neonatal biomagnetism Citation: Gutiérrez D, García-Guevara F, Kiefer I, Draganova R and Preissl H (2010). Characterizing fetal sympatho-vagal balance through multivariate time-varying autoregressive modeling of magnetocardiographic data. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00135 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 25 Mar 2010; Published Online: 25 Mar 2010. * Correspondence: D. Gutiérrez, Centro de Investigación y de Estudios Avanzados, Apodaca, Mexico, dgtz@ieee.org Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers D. Gutiérrez F M García-Guevara I Kiefer R. Draganova H Preissl Google D. Gutiérrez F M García-Guevara I Kiefer R. Draganova H Preissl Google Scholar D. Gutiérrez F M García-Guevara I Kiefer R. Draganova H Preissl PubMed D. Gutiérrez F M García-Guevara I Kiefer R. Draganova H Preissl Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Simple linear regression models have been widely employed in the analysis of suspended-sediment concentration (SSC) time series from glacierized catchments, although they have many limitations. This paper builds regression models which address these shortcomings and permit inferences concerning the controls on suspended-sediment transfer from a glacier at 78°N in the Svalvard archipelago. A bivariate regression model, deterministically predicting SSC from discharge alone, explained less than 15 per cent of the variance in SSC. A multivariate model, incorporating additional potentially explanatory variables, offered little improvement. Diurnal hysteresis in the data gives rise to quasi-autocorrelation in the residual series from regression models. This was effectively removed by incorporating dummy diurnal variables into the multivariate model. The presence of a first-order autoregressive, stochastic process gives rise to true autocorrelation in the residual series from regression models. This was accommodated by incorporating an ARIMA (1,0,0) term into a multivariate autoregression model. The model-building process yielded a systematic progression in the explanation of variance in SSC, stripping away pattern in the autocorrelation function of the residual series; mean model error was reduced from 54 per cent to 6 per cent. The dependence of SSC on the magnitude of discharge is weak and highly variable, whereas the dependence of current SSC on recent values of SSC, revealed through the stochastic term, is an order of magnitude greater and relatively constant during the melt season. The dominant control on SSC throughout the melt season is therefore short-term sediment availability. The simple and largely unchanging stochastic process generally responsible for generating the observed SSC series implies a simple and unchanging glacier drainage system. Copyright © 1999 John Wiley & Sons, Ltd.

Linear multivariate models for physiological signal analysis: theory

Automated classification of non-motor mental task in electroencephalogram based brain-computer interface using multivariate autoregressive model in the intrinsic mode function domain

Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models

Time series subject to regime shifts have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, models such as the popular Hidden Markov Chain (HMC) describe time series whose state process is unknown at all time-steps. Sometimes, time series are annotated. Thus, another category of models handles the case with regimes observed at all time-steps. We present a novel model which addresses the intermediate case: (i) state processes associated to such time series are modelled by Partially Hidden Markov Chains (PHMCs); (ii) a multivariate linear autoregressive (MLAR) model drives the dynamics of the time series, within each regime. We describe a variant of the expectation maximization (EM) algorithm devoted to PHMC-MLAR model learning. We propose a hidden state inference procedure and a forecasting function adapted to the semi-supervised framework. We first assess inference and prediction performances, and analyze EM convergence times for PHMC-MLAR, using simulated data. We show the benefits of using partially observed states as well as a fully labelled scheme with unreliable labels, to decrease EM convergence times. We highlight the robustness of PHMC-MLAR to labelling errors in inference and prediction tasks. Finally, using turbofan engine data from a NASA repository, we show that PHMC-MLAR outperforms or largely outperforms other models: PHMC and MSAR (Markov Switching AutoRegressive model) for the feature prediction task, PHMC and five out of six recent state-of-the-art methods for the prediction of machine useful remaining life.

Coupled annual and daily multivariate and multisite stochastic weather generator to preserve low- and high-frequency variability to assess climate vulnerability

. This article presents a Bayesian method for obtaining forecasts based on a multivariate threshold autoregressive (MTAR) model with a multivariate Student’s t error distribution. We derive the Bayesian predictive distribution, which incorporates uncertainty about the true values of the MTAR model parameters. The proposed procedure involves drawing samples from the predictive distribution to obtain point forecasts and prediction intervals for each univariate component of the multivariate process of interest. Although the model accounts for the multivariate nature of the data, the prediction intervals are constructed individually for each variable. We verify the performance of the proposed algorithm through a simulation study based on three models, calculating the percentage of times the true values of each component of the output process fall within the 95% individual prediction intervals of the predictive distribution. Additionally, we present an application to a set of financial time series, where forecasts of the returns of the Bovespa and Colcap indexes are obtained using the returns of the Standard and Poor’s 500 index as the threshold variable.

In this study, we investigate the impacts of common information between oil futures and the United States stock markets on forecasting oil volatility using the multivariate heterogeneous autoregressive realized volatility model. We have several noteworthy findings. First, the in‐sample estimation results show that the negative returns and the ‘bad’ jumps have larger influence on oil futures volatility than positive returns and ‘good’ jumps, respectively. Second, the out‐of‐sample results further indicate that our multivariate heterogeneous autoregressive (HAR) model can generate higher forecast accuracy than individual HAR model for the realized volatility‐type models, which highlights the importance of incorporating volatility information from the stock Market. Third, our findings are robust across the direction‐of‐change test and different windows. Furthermore, from the perspective of the investors' allocation portfolio in the future, the use of common information can also bring greater gains.

In recent years, there are growing interests in developing novel approaches for inferring dynamic interactions in biological systems including gene transcription network and microbial interaction networks. Multivariate Vector Autoregression (MVAR) model is one of these efficient methods. Variants of MVAR with different penalties or regularizations can avoid the problem of over-fitting and provide great potential in high-dimensional data analysis. In this paper, we developed a novel regularization methods for MVAR via weighted fusion which consider the correlation among variables. The weighted fusion can potentially incorporate information redundancy among correlated variables for estimation and variable selection. Weighted fusion is also useful when the number of predictors p is larger than the number of observations n. In theory, we discuss the grouping effect of weighted fusion regularization for linear models. We then apply the proposed model on several time series data sets especially a time series dataset of human gut microbiomes. The experimental results indicate that the new approach has better performance that several other VAR-based models and we demonstrate its capability of extracting relevant microbial interactions.

We test the adequacies of several proposed and two new statistical methods for recovering the causal structure of systems with feedback from synthetic BOLD time series. We compare an adaptation of the first correct method for recovering cyclic linear systems; Granger causal regression; a multivariate autoregressive model with a permutation test; the Group Iterative Multiple Model Estimation (GIMME) algorithm; the Ramsey et al. non-Gaussian methods; two non-Gaussian methods by Hyvärinen and Smith; a method due to Patel et al.; and the GlobalMIT algorithm. We introduce and also compare two new methods, Fast Adjacency Skewness (FASK) and Two-Step, both of which exploit non-Gaussian features of the BOLD signal. We give theoretical justifications for the latter two algorithms. Our test models include feedback structures with and without direct feedback (2-cycles), excitatory and inhibitory feedback, models using experimentally determined structural connectivities of macaques, and empirical human resting-state and task data. We find that averaged over all of our simulations, including those with 2-cycles, several of these methods have a better than 80% orientation precision (i.e., the probability of a directed edge is in the true structure given that a procedure estimates it to be so) and the two new methods also have better than 80% recall (probability of recovering an orientation in the true structure).